The Topological G/G WZW Model in the Generalized Momentum Representation

TL;DR

This paper reformulates the topological gauged WZW model using Poisson sigma-models, revealing new insights into gauge dependence, topological invariance, and the emergence of Quantum Groups.

Contribution

It introduces a novel formulation of the GWZW model as a Schwarz type topological theory using Poisson sigma-model techniques.

Findings

Explicit evaluation of the gauge cocycle _{GWZW}

Proof of metric independence for genus one, conjecture for higher genus

New explanation for Quantum Groups in the WZW model

Abstract

We consider the topological gauged WZW model in the generalized momentum representation. The chiral field $g$ is interpreted as a counterpart of the electric field $E$ of conventional gauge theories. The gauge dependence of wave functionals $\Psi(g)$ is governed by a new gauge cocycle $\phi_{GWZW}$. We evaluate this cocycle explicitly using the machinery of Poisson $\sigma$-models. In this approach the GWZW model is reformulated as a Schwarz type topological theory so that the action does not depend on the world-sheet metric. The equivalence of this new formulation to the original one is proved for genus one and conjectured for an arbitrary genus Riemann surface. As a by-product we discover a new way to explain the appearance of Quantum Groups in the WZW model.